WDVV equation and Triple-product Relation

Abstract

We study the relation between the WDVV equations and the $\tau$-function of the noncommutative KP (NCKP) hierarchy. WDVV-like equations (Hirota triple-product relation) in the noncommutative context appear as a consequence of the non-trivial equation for $\tau$-function of the NC KP hierarchy, while the prepotential in the Seiberg-Witten (SW) theory has been identified to the $\tau$-function of the Whitham hierarchy. We show that the spectral curve for the SW theory is the same as the Toda-chain hierarchy. We also show that Whitham hierarchy includes commutative Toda/KP hierarchy as a construction. Further, we comment on the origin of the Hirota triple-product relation in the context of the SW theory.

Latex,11 pages,no figures

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Cited by in corpus (2)

• On Reductions of Noncommutative Anti-Self-Dual Yang-Mills Equations
• Extension of Moyal-deformed hierarchies of soliton equations